It takes precisely 3 cooks, C, and 5 units of food, F. to produce a single Five course meal. The price of a cook is 100 and the price of food is 50 per unit of food. Determine both the production function and the cost function.

the production function always follows this pattern: Q = K + L

Q = quantity of output

K = quantity of capital

L = quantity of labor

in this case, since you need 3 cooks and 5 units of food to prepare 5 meals, the production function is:

M = 3C + 5F

where;

M = five course meal

C = cooks

F = units of food

the cost function always follows this pattern: C = FC + VC

C = total production cost

FC = fixed costs

VC = variable costs

since the price of a cook is 100 per cook and the price of food is 50 per food unit, the production cost function is:

M = 100L + 50F

where:

C = production cost of a course meal

L = number of cooks required

F = units of food required

C = ($100 x 3) + ($50 x 5) = $550

in this case we were only given variable costs, so this cost function does not include any fixed costs.